本题目来源于试卷: IB MAI HL Functions Topic 2.3 Properties of Functions，类别为 IB数学
[问答题]
A cable making machi- 7+uhvvr/tga4w fz9y ne in 9fen0f7hjr0ul ee3 ;ia factory produces 5 metres of cable every 3 minutes. After 4 hours of continjr;3fl e0 e7en0u 9ihfuous use, the machine requires 48 minutes of preventative maintenance. Apart from this preventative maintenance, the machine works continuously without interruption.
1.Determine the function, $L$, that represents the length of cable produced in terms of time, t, measured in days.
The company sells the cable it produces and has found that the income (in dollars) from selling L metres of cable can be modelled by the function
$I(L)=(3−\sqrt{7})L−500$2.Determine a function for income, I, in terms of time, t, in days.
The company is considering an investment in a new machine that produces 6 metres of cable every 3 minutes and needs 60 minutes of preventive maintenance for every 7 hours of use.
3.Show that the income function for this new machine, in terms of the number of days, t, can be expressed as.
$I_2(t)=(3−\sqrt{7})(2520t)−500$
4.Determine a function, D, to model the difference in incomes between the two machines, in terms of the number of days, t.
The company decides to purchase the new machine only if it can recover the cost of the machine through the difference in incomes over six month period (assume 180 days).
5.Find the highest amount the company will be willing to pay for the new machine, rounded to the nearest dollar.
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